The Sigma–Schmidt Tri-Cosmology: Dimensional Genesis, Energetic Duality, and the Spiral Unfolding of Three-Dimensional Space

This paper introduces the Sigma–Schmidt Tri-Cosmology, a unified and dynamically constrained framework in which three-dimensional space emerges from the coupled evolution of two fundamental energetic axes: the one-dimensional extraction axis SeS_eSe and the two-dimensional expansion sheet SaS_aSa. Their interaction generates the volumetric field σ(t)=SeSaσ(t) = S_e S_aσ(t)=SeSa, whose temporal dynamics reproduce the observed spiral-like, layered, and resonant structures in astrophysical and cosmological data. The work extends the core Sigma–Schmidt Duality by deriving the Dimensional Genesis (1D → 2D → 3D → 4D time-layering), the energetic duality equations, and a spiral-unfolding model that predicts large-scale signatures such as: helical angular-momentum bands, GRB angular clustering, spiral-time redshift modulation, volumetric resonance patterns, and multi-scale emergence across cosmic structures. The theory provides a geometric and physically motivated mechanism for the genesis of three-dimensional space, grounded in dimensional friction, resonant transfer, and the feedback cycle between SeS_eSe and SaS_aSa. This Tri-Cosmology paper forms one of the central theoretical pillars of the Sigma–Schmidt framework and connects cosmological expansion, geometric evolution, and emergent structure formation into a single coherent picture.